get_option returning a different value from what’s saved

In the plugin_options_validate() function the return value of get_option( 'plugin_options' ) is never used.

Let’s step through the function by adding some comments:

// Retrieve the options.
$options = get_option('plugin_options');

// Replace the options without checking if
// trim( $input['text_string'] ) and trim( $input['text_string_name'] )
// actually return strings and if $input['text_string'] and 
// $input['text_string_name'] have anything in them.
$options['text_string'] = trim($input['text_string']);
$options['text_string_name'] = trim($input['text_string_name']);

// This part never runs. `$options` will never be empty!
if ( empty( $options ) ) {
    $options['text_string'] = '[email protected]';
    $options['text_string_name'] = 'Polyindustry';
}

Effectively, this function is the same thing you have written:

// Validate options.
function plugin_options_validate( $input ) {

    $options['text_string'] = trim( $input['text_string'] );
    $options['text_string_name'] = trim( $input['text_string_name'] );

    return $options;
}